Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)William Somerville Orr W.S. Orr and Company, 1854 |
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Seite 48
... draw CA , CB , * the triangle ABC shall * Post , 1 . be equilateral . + Def . 12 . * Ax . 1 . Because A is the ... draw a straight line ( AL ) equal to a given straight line ( BC ) . • Post . 1. From A to B draw AB , * and upon AB ...
... draw CA , CB , * the triangle ABC shall * Post , 1 . be equilateral . + Def . 12 . * Ax . 1 . Because A is the ... draw a straight line ( AL ) equal to a given straight line ( BC ) . • Post . 1. From A to B draw AB , * and upon AB ...
Seite 50
... draw F C , G B. * Pr . 3 . + Const . * Hyp . Because FAG A , † and AC = A B * ... F A , A C are equal to GA , AB , each to each ; and the angle A is common to both the triangles AFC , AGB ; .. FC = GB , † the angle + Pr . 4 . ACF the ...
... draw F C , G B. * Pr . 3 . + Const . * Hyp . Because FAG A , † and AC = A B * ... F A , A C are equal to GA , AB , each to each ; and the angle A is common to both the triangles AFC , AGB ; .. FC = GB , † the angle + Pr . 4 . ACF the ...
Seite 52
... draw DE , and + Pr . 1. upon it describe an equilateral triangle DEF , † so that the vertex F may be on the opposite side of D E to the vertex A. Draw A F , then AF shall bisect the angle BAC . * Const . Because AD AE , * and that AF is ...
... draw DE , and + Pr . 1. upon it describe an equilateral triangle DEF , † so that the vertex F may be on the opposite side of D E to the vertex A. Draw A F , then AF shall bisect the angle BAC . * Const . Because AD AE , * and that AF is ...
Seite 53
... Draw CF , CG . Then because FH = * Const . GH , * and HC common to the two triangles FHC , GHC , the two sides FH , HC are the two sides GH , HC , cach to each , and the base CF = the base + Def . 12. CG ; † .. the angle CHF the ...
... Draw CF , CG . Then because FH = * Const . GH , * and HC common to the two triangles FHC , GHC , the two sides FH , HC are the two sides GH , HC , cach to each , and the base CF = the base + Def . 12. CG ; † .. the angle CHF the ...
Seite 57
... draw DE . Make the triangle AF G , the sides of which shall be equal to those of CDE , namely , AFCD , AG = CE , and FG- * Pr . 22. DE ; * then the angle A shall be equal to C. Because AFC D , A G = C E , and FG = * Pr . 8. DE , .. the ...
... draw DE . Make the triangle AF G , the sides of which shall be equal to those of CDE , namely , AFCD , AG = CE , and FG- * Pr . 22. DE ; * then the angle A shall be equal to C. Because AFC D , A G = C E , and FG = * Pr . 8. DE , .. the ...
Häufige Begriffe und Wortgruppen
ABCD Algebra arithmetic base Binomial Theorem bisect calculation called centre chord circumference coefficient common Completing the square contained cotan decimals denominator describe diameter divided dividend divisor draw ellipse equal angles equation equiangular equilateral Euclid EXAMPLES FOR EXERCISE expression exterior angle factors figure formula fraction frustum geometrical progression geometry given straight line greater h₂ Hence inscribed intersecting join latter less logarithm magnitudes manner measure multiplied operation parallel parallelogram perpendicular plane polygon prism Prop proportion proved Q. E. D. PROPOSITION quantity quotient radius ratio rectangle remainder result right angles rule sides sines solid angle sphere square root subtract suppose theorem third triangle ABC trigonometrical
Beliebte Passagen
Seite 86 - If two triangles have two sides of the one equal to two sides of the...
Seite 60 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Seite 58 - ... equal angles in each ; then shall the other sides be equal each to each : and also the third angle of the one to the third angle of the other.
Seite 45 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Seite 190 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Seite 47 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 151 - Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional ; and parallelograms that have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Seite 96 - angle in a segment' is the angle contained by two straight lines drawn from any point in the circumference of the segment, to the extremities of the straight line which is the base of the segment.
Seite 46 - A rhombus, is that which has all its sides equal, but its angles are not right angles.
Seite 66 - From this it is manifest how to a given straight line to apply a parallelogram, which shall have an angle equal to a given rectilineal angle, and shall be equal to a given rectilineal figure, viz.